This research is concerned with the study of invariants for torsion-free abelian groups of finite rank and finite valuated p- groups. Successful completion of this project will result in a complete set of invariants for a large class of mixed abelian groups that includes the class of Warfield groups. Other areas of investigation include the connection with vector space representations of finite partially ordered sets, the structure of torsion-free abelian groups that are flat as modules over their endomorphism ring, and E-modules. This project is in the general area of abelian group theory and is concerned with the classification of abelian groups. Although the classification of finite abelian groups has been well understood for a century, the classification of infinite abelian groups remains elusive. This research involves this old problem of classification of the infinite abelian groups, approached with new techniques.
